Factor (2+x)^3-8

${(2 + x)}^{3} - 8$

Rewrite $8$ as $2^{3}$ .

${(2 + x)}^{3} - 2^{3}$

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 2 + x$ and $b = 2$ .

$(2 + x - 2) ({(2 + x)}^{2} + (2 + x) \cdot 2 + 2^{2})$

Simplify.

Subtract $2$ from $2$ .

$(x + 0) ({(2 + x)}^{2} + (2 + x) \cdot 2 + 2^{2})$

Add $x$ and $0$ .

$x ({(2 + x)}^{2} + (2 + x) \cdot 2 + 2^{2})$

Rewrite ${(2 + x)}^{2}$ as $(2 + x) (2 + x)$ .

$x ((2 + x) (2 + x) + (2 + x) \cdot 2 + 2^{2})$

Expand $(2 + x) (2 + x)$ using the FOIL Method.

Apply the distributive property.

$x (2 (2 + x) + x (2 + x) + (2 + x) \cdot 2 + 2^{2})$

Apply the distributive property.

$x (2 \cdot 2 + 2 x + x (2 + x) + (2 + x) \cdot 2 + 2^{2})$

Apply the distributive property.

$x (2 \cdot 2 + 2 x + x \cdot 2 + x \cdot x + (2 + x) \cdot 2 + 2^{2})$

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$x (4 + 2 x + x \cdot 2 + x \cdot x + (2 + x) \cdot 2 + 2^{2})$

Move $2$ to the left of $x$ .

$x (4 + 2 x + 2 x + x \cdot x + (2 + x) \cdot 2 + 2^{2})$

Multiply $x$ by $x$ .

$x (4 + 2 x + 2 x + x^{2} + (2 + x) \cdot 2 + 2^{2})$

Add $2 x$ and $2 x$ .

$x (4 + 4 x + x^{2} + (2 + x) \cdot 2 + 2^{2})$

Apply the distributive property.

$x (4 + 4 x + x^{2} + 2 \cdot 2 + x \cdot 2 + 2^{2})$

Multiply $2$ by $2$ .

$x (4 + 4 x + x^{2} + 4 + x \cdot 2 + 2^{2})$

Move $2$ to the left of $x$ .

$x (4 + 4 x + x^{2} + 4 + 2 x + 2^{2})$

Raise $2$ to the power of $2$ .

$x (4 + 4 x + x^{2} + 4 + 2 x + 4)$

Add $4$ and $4$ .

$x (4 x + x^{2} + 8 + 2 x + 4)$

Add $4 x$ and $2 x$ .

$x (6 x + x^{2} + 8 + 4)$

Add $8$ and $4$ .

$x (6 x + x^{2} + 12)$

Reorder terms.

$x (x^{2} + 6 x + 12)$

Factor (2+x)^3-8

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